Algebraic models defined over Q of differential manifolds

Here we prove that every compact differential manifold has a smooth algebraic model defined over Q. In dimension 2 we find an algebraic model (may be singular) defined over Q and birational over Q to the projective plane.     

On uniformly Gâteaux smooth norms and normal structure

It is shown that every separable Banach space admits an equivalent norm that is uniformly Gâteaux smooth and yet lacks asymptotic normal structure.

     

The homotopy categorical crossed module of a CW-complex

Crossed modules have longstanding uses in homotopy theory and the cohomology of groups. The corresponding notion in the setting of categorical groups, that is, categorical crosses modules, allowed the development of a low-dimensional categorical group cohomology. Now, its relevance is also shown here to homotopy types by associating, to any pointed CW-complex (X,∗), a categorical crossed module that algebraically represents the homotopy 3-type of X.     

The 1-type of a Waldhausen K-theory spectrum

We give a small functorial algebraic model for the 2-stage Postnikov section of the K-theory spectrum of a Waldhausen category and use our presentation to describe the multiplicative structure with respect to biexact functors.     

Random orderings of the integers and card shuffling

In this paper we study random orderings of the integers with a certain invariance property. We describe all such orders in a simple way. We define and represent random shuffles of a countable set of labels and then give an interpretation of these orders in terms of a class of generalized riffle shuffles.     

Recognition of Monohydrogen Anions of Geometrical and Positional Isomers of Dicarboxylic Acids Based on Polymeric Liquid Membranes Incorporating Polyamine Host

Macrocyclic lipophilic polyamines were applied as the sensory elements of polymeric liquid membrane electrodes. These hosts gain the anion receptor functionality upon protons uptake from the aqueous solutions. The electrodes studied were able to distinguish potentiometricaly isomers of monocharged and doublecharged forms of ethylene and benzene dicarboxylic acids. The selectivity of interaction between protonated hosts and anionic guests relays not only on the electrostatic interactions, but on hydrogen bounds formations as well. The influence of lipophilicity of protonated hosts on the potential response generation was discussed.     

Sur la R-équivalence de torseurs sous un groupe fini

We give criteria for R-equivalence of torsors under finite constant group schemes over a field. In particular, using bitorsors, we obtain a Galois dévissage result which formalises and generalises a theorem of Philippe Gille in the case of local fields; for instance, Gille's theorem is shown to extend to higher local fields.     

Optimal prediction for linear regression with infinitely many parameters

The problem of optimal prediction in the stochastic linear regression model with infinitely many parameters is considered. We suggest a prediction method that outperforms asymptotically the ordinary least squares predictor. Moreover, if the random errors are Gaussian, the method is asymptotically minimax over ellipsoids in ?₂. The method is based on a regularized least squares estimator with weights of the Pinsker filter. We also consider the case of dynamic linear regression, which is important in the context of transfer function modeling.     

The representation type of Hecke algebras of type B

This paper determines the representation type of the Iwahori-Hecke algebras of type B when q≠±1. In particular, we show that a single parameter non-semisimple Iwahori-Hecke algebra of type B has finite representation type if and only if q is a simple root of the Poincaré polynomial, confirming a conjecture of Uno's (J. Algebra 149 (1992) 287).